Factorise:
p4 - 81
We have p4 - 81 = (p2)2 - (92)2
Now using a2 - b2 = (a + b)(a - b), we have
(p2)2 - (9)2 = (p2 + 9)(p2 -9)
We can factorise p2 - 9 further as
p2 - 9 = (p)2 - (3)2
= (p + 3)(p - 3)
∴ p4 - 81 = (p + 3)(p - 3)(p2 + 9)